Changing location of a walk cycle keyframe
So I guess you must have keyframed the armature's location itself. What you need to do is open the Graph Editor, unfold the Object Transforms tracks, select the track that you need to change (probably X or Y Location), press ShiftH to hide all the other tracks (AltH to bring them back later) and move the curve on the Graph Editor X or Y axis. It will only work if the duplicated action is a simple copy and not a linked duplication, in that case you need to click on New Action in the Dope Sheet.